Based on analyzing the properties of Bernstein polynomials, the extended orthonormal Bernstein polynomials, defined on the interval [0, 1] for n=7 is achieved. Another method for computing operational matrices of derivative and integration D_b and R_(n+1)^B respectively is presented. Also the result of the proposed method is compared with true answers to show the convergence and advantages of the new method.

    This work is concerned with studying the solvability for optimal classical continuous control quaternary vector problem that controls by quaternary linear hyperbolic boundary value problem. The existence of the unique quaternary state vector solution for the quaternary linear hyperbolic boundary value problem  is studied and demonstrated by employing the method of Galerkin, where the classical continuous control quaternary vector  is Known. Also, the existence theorem of an optimal classical continuous control quaternary vector related to the quaternary linear hyperbolic boundary value problem is demonstrated. The existence of a unique solution to the adjoint quaternary linear hyperbolic boundary value problem a

In this work, nonlinear diabetes controlled model with and without complications in a population is considered. The dynamic behavior of diabetes in a population by including a constant control is studied and investigated. The existence of all its possible fixed points is investigated as well as the conditions of the local stability of the considered model are set. We also find the optimal control strategy in order to reduce the number of people having diabetes with complications over a finite period of time. A numerical simulation is provided and confirmed the theoretical results.

For many problems in Physics and Computational Fluid Dynamics (CFD), providing an accurate approximation of derivatives is a challenging task. This paper presents a class of high order numerical schemes for approximating the first derivative. These approximations are derived based on solving a special system of equations with some unknown coefficients. The construction method provides numerous types of schemes with different orders of accuracy. The accuracy of each scheme is analyzed by using Fourier analysis, which illustrates the dispersion and dissipation of the scheme. The polynomial technique is used to verify the order of accuracy of the proposed schemes by obtaining the error terms. Dispersion and dissipation errors are calculated

Human beings are greatly inspired by nature. Nature has the ability to solve very complex problems in its own distinctive way. The problems around us are becoming more and more complex in the real time and at the same instance our mother nature is guiding us to solve these natural problems. Nature gives some of the logical and effective ways to find solutions to these problems. Nature acts as an optimized source for solving the complex problems.  Decomposition is a basic strategy in traditional multi-objective optimization. However, it has not yet been widely used in multi-objective evolutionary optimization.   

Although computational strategies for taking care of Multi-objective Optimization Problems (MOPs) h

Many numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.

A simple, precise and accurate spectrophotometric method has been developed for simultaneous estimation of sulfanilamide and furosemide in their mixture by using first and second order derivative method in the ultraviolet region. The method depends on first and second derivative spectrophotometry, with zero-crossing and peak to base line and peak area measurements. The first derivative amplitudes at 214, 238 and 266 nm were selected for the assay of sulfanilamide and 240, 260, 284, 314 and 352 nm for furosemide. Peak area at 201222, 222-251 and 251-281 nm selected for estimation of sulfanilamide and at 229-249, 249270, 270-294, 294-333 and 333-382 nm for furosemide. The second derivative amplitudes at 220, 252 and 274 nm for sulfanilamid

The fuzzy sets theory has been applied in many fields, such as operations research, control theory and management sciences, etc. In particular, an application of this theory in decision making problem is linear programming problems with fuzzy technological coefficients numbers, as well as studying the parametric linear programming problems in the case of changes in the objective function. In this paper presenting a new procedure which connects and makes link between fuzzy linear programming problem with fuzzy technological coefficients numbers and parametric linear programming problem with change in coefficients of the objective function, then develop a numerical example illustrates the steps of solution to this kind of problems.